Yeah, but nobody tries to prove anything that can't logically be proven. So not only is there no replicability crisis but such a thing can't exist in the first place.
People try all the time to prove things that can't logically be proven. Probably lifetimes spent on Euclid's parallel postulate alone - over 2000 years of attempts! Before Russell Frege thought his logic was consistent. Before Gödel it was believed we could formalize a complete arithmetic even if Frege's specific design failed. Before Church and Turing the Entscheidungsproblem was considered potentially solvable even if Gödel's work ruled out the resultant proofs wholly capturing powerful theories.
It took a very long time to even notice the axiom of choice, and longer to ultimately prove its proof futile.
What I'm saying is no papers are written about it unless the author made a mistake. In the absence of a genuine logical mistake, no replicability crisis is possible.
